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Asymptotic Notations Algorithms perform f(n) basic operations to accomplish task Identify that function Identify size of problem (n) Count number of operations.

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Presentation on theme: "Asymptotic Notations Algorithms perform f(n) basic operations to accomplish task Identify that function Identify size of problem (n) Count number of operations."— Presentation transcript:

1 Asymptotic Notations Algorithms perform f(n) basic operations to accomplish task Identify that function Identify size of problem (n) Count number of operations in terms of n

2 Execution time Time computer takes to execute f(n) operations is cf(n)
where c depends on speed of computer and varies from computer to computer

3 Development of Notation
Not concerned with small values of n Concerned with VERY LARGE values of n Asymptotic – refers to study of function f as n approaches infinity Example: f(n) = n2+4n + 20 n2 is the dominant term and the term 4n + 20 becomes insignificant as n grows larger

4 Development of Notation
Drop insignificant terms and constants Say function is of O(n2) called Big-O of n2 Common Big-O functions in algorithm analysis g(n) = 1 (growth is constant) g(n) = log 2 n (growth is logarithmic) g(n) = n (growth is linear) g(n) = n log 2 n (growth is faster than linear) g(n) = n2 (growth is quadratic) g(n) = 2n (growth is exponential)

5 n log2n nlog2n n^2 2^n 1 2 4 8 16 3 24 64 256 65536 32 5 160 1024

6 Common Growth Functions (How f(n) grows as n grows)


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